三角代数上的可乘映射

Multiplicative maps on triangular algebras

为了研究在两个代数之间的固定点上可乘的可加映射什么时候是任意点可乘的,本文利用矩阵运算技巧,在三角代数范畴上证明了两个三角代数之间的可加满射在固定点可乘时一定是可乘的。最后将该结果应用到了Hilbert空间的套代数上。

In order to study the problem when a linear map that is multiplicative at a fixed point is a multiplicative map between two algebras,we use the techniques for matrix operation to prove that every linear surjective map which is multiplicative at a fixed point is a multiplicative map on triangular algebras.The result is applied to the nest algebras of Hilbert space.